Object moves but the location doesn't change
There's a ClampTo constraint on the object jumping there around and this constraint has its Influence option keyframed to become 0 at that frame:



Thus at that frame the constraint stops influence the object and it changes its position. You can edit keyframes' values or delete them to avoid jumping.

Also note that location of the object by X axis which is also keyframed has quite rough animation curve:



You might need to change the curve to make that moment correlate with the rest of the animation.